Open House, ISM in National Center of Sciences Building, 2019.6.05統計数理研究所オープンハウス（学術総合センター）、R1.6.5ポスター発

Jiancang Zhuang

庄 建倉

English

RISM (Repository of the Institute of Statistical Mathematics) / 統計数理研究所 学術研究リポジトリ

マーク付き点過程の欠損データのテスト及び補完Detection and replenishment of missing data for marked point processes庄 建倉 モデリング研究系 准教授2019年6月5日 統計数理研究所 オープンハウス【Aim】 This project presents a fast approach for replenishing missing data in the record of a temporal point process with time separable marks, such as records of earthquakes and volcanic eruptions, in order to eliminate the underestimate of corresponding hazards caused by missing data. 【What is a point process】Point process: random patterns of discreet events in space and/or time. Marked point process: each event is assigned an attribute or size, namely a mark.Conditional intensity: 𝜆 𝑡,𝑚 ∣ 𝐻𝑡 𝑑𝑡 𝑑𝑚 = 𝐄 [𝑁 𝑡, 𝑡 + 𝑑𝑡 × 𝑚,𝑚 + 𝑑𝑚 𝐻𝑡Mark-separable marked point process: 𝜆 𝑡,𝑚 ∣ 𝐻𝑡 = 𝜆𝑔 𝑡 ∣ 𝐻𝑡 𝑓 𝑚𝐻𝑡: observation history up to time t.【Bi-scale empirical transformation】Bi-scale empirical transformation transforms a mark-separable point process 𝑁 = 𝑡𝑖 , 𝑚𝑖 : 𝑖 = 1,⋯𝑁 on 0, 𝑇 × 𝐌into a homogeneous pattern on the unit square.Γ: 0, 𝑇 × 𝐌 → 0,1 × [0,1]𝑡,𝑚 → ෨𝐹 𝑡 , ෨𝐺 𝑚෨𝐹 𝑡 , ෨𝐺 𝑚 : empirical distribution function of 𝑡𝑖: 𝑖 = 1,⋯𝑁 and 𝑚𝑖: 𝑖 = 1,⋯𝑁【Testing methods】Testing results for (*)【Replenish Algorithm】Homogeneous process Original  complete  process Non-homogeneous process Original  incomplete  process 𝑅 =min 𝐶1, 𝐶2, ⋯ , 𝐶𝐿max 𝐶1, 𝐶2, ⋯ , 𝐶𝐿𝐷 = max 𝐶1, 𝐶2, ⋯ , 𝐶𝐿 −min 𝐶1, 𝐶2, ⋯ , 𝐶𝐿𝐿 = #𝑅𝑜𝑤 × #𝐶𝑜𝑙𝑢𝑚𝑛𝐶𝑖: number of events at each cellsStep 1. Transform the process  using the biscale empirical transformation.𝑡𝑖 → 𝜏𝑖 =𝑖𝑁=# 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 < 𝑡𝑖𝑁𝑚𝑖 → 𝑠𝑖 =σ𝑘 𝟏(𝑚𝑘 < 𝑚𝑖)𝑁=# 𝑜𝑓 𝑚𝑎𝑟𝑘𝑠 < 𝑚𝑖𝑁Step 2. Specify area S that contains the missing data in in the initial transformation domain.Step 3. Calculate the missing area  𝑆∗ in biscale transformation domain by solving𝐹1∗ 𝑡 =σ𝑗=1𝑛 𝑤1 𝑡𝑗 , 𝑚𝑗 , 𝑆 𝟏 𝑡𝑗 < 𝑡σ𝑗=1𝑛 𝑤1 𝑡𝑗 , 𝑚𝑗 , 𝑆𝐹2∗ 𝑚 =σ𝑗=1𝑛 𝑤2 𝑡𝑗 , 𝑚𝑗 , 𝑆 𝟏 𝑚𝑗 < 𝑚σ𝑗=1𝑛 𝑤2 𝑡𝑗 , 𝑚𝑗 , 𝑆𝑤1 𝑡,𝑚, 𝑆 =𝟏 𝑡,𝑚 ∉ 𝑆׬𝑀 𝟏 𝑡, 𝑠 ∉ 𝑆 𝑑𝐹2∗ 𝑠𝑤2 𝑡,𝑚, 𝑆 =𝟏 𝑡,𝑚 ∉ 𝑆׬𝑀 𝟏 𝜏,𝑚 ∉ 𝑆 𝑑𝐹1∗ 𝜏𝑆∗ = {𝐹1∗ 𝑡 , 𝐹2∗ 𝑚 : 𝑡,𝑚 ∈ 𝑆}Step 4. Generate data point in the missing areaGenerate events uniformly distributed in the missing region S* (image of S)# events ~ 𝑁𝐵 𝑘, 1 − 𝑆∗𝑘: # of observed events outside of 𝑆∗Step 5. Remove sequentially the closest simulated data point for each existing point in the missing area.Step 5. Transform back all the events into the original domain【Example 1:  Eruptions at Hakone volcano】【Example 2: Recent Kumamoto earthquake sequence data】Data source: (1) Smithsonian's Global Volcanism Program database (2) Large Magnitude Explosive Volcanic Eruptions database (LaMEVE database) (3) additional Japanese databasesData: Japan Meteorological Agency catalogTime:   2016/4/1~2016/4/21  Mag.:   1.0+Depth:  < 100 km                  Space:  E128° - 133°N30°-- 35°Observed data Biscale transformationEstimated transformation under complete dataTransformed replenished data Replenished data Cumulative freq. vs timeObserved data Biscale transformationEstimated transformation under complete dataTransformed replenished data Replenished data Cumulative freq. vs time(*)

マーク付き点過程の欠損データのテスト及び補完

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マーク付き点過程の欠損データのテスト及び補完

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RISM (Repository of the Institute of Statistical Mathematics) / 統計数理研究所学術研究リポジトリ

マーク付き点過程の欠損データのテスト及び補完

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RISM (Repository of the Institute of Statistical Mathematics) / 統計数理研究所 学術研究リポジトリ

RISM (Repository of the Institute of Statistical Mathematics) / 統計数理研究所学術研究リポジトリ